The present ratio of ages of P and Q is 2 : 7. Six years ago, this ratio was 1 : 5. Determine the present age of P?

16 years

The correct answer is Option (4) → 16 years

Step 1: Let the present ages be

Let present ages of P and Q be:

$P = 2x, \quad Q = 7x$

(as the ratio is 2 : 7)

Step 2: Use the information from 6 years ago

Six years ago:

$\frac{P - 6}{Q - 6} = \frac{1}{5}$

Substitute $P = 2x$ and $Q = 7x$:

$\frac{2x - 6}{7x - 6} = \frac{1}{5}$

Step 3: Solve for x

$5(2x−6)=1(7x−6)$

$10x−30=7x−6$

$10x - 7x = -6 + 30$

$3x = 24$

$x = 8$

Step 4: Find present age of P

$P = 2x = 2 \times 8 = 16 \text{ years}$